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If you use NumPy for numerical computations, which I recommend if you program in Python, one of the key things to do is to process entire arrays in one go as much as possible (this is also true for MATLAB). Using these so-called vectorized operations makes sure that… read more

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Say that you have implemented a low-pass FIR filter with the correct cut-off frequency and transition band, but that you are not quite happy with the suppression of frequencies in the stop band. A straightforward trick to put in your toolbox is that you can double the suppression by… read more

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In my articles on filter design I mostly focus on a rather specific subset of all possible filters, namely symmetrical FIR filters with an odd number of coefficients. Each of these properties (1. FIR, 2. symmetrical, and 3. an odd number of coefficients) was chosen for… read more

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ʻOumuamua is the first ever interstellar body that was observed while it passed through our solar system, which makes it a really cool object. Hundreds of thousands of asteroids and comets have been observed, but all of them originated from within our own solar system. It was known that… read more

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A Hadamard matrix is a matrix with all elements equal to \(+1\) or \(-1\), and for which the rows are mutually orthogonal. If you pick two rows from the matrix and write it as vectors \(\bf x\) and \(\bf y\), then these are orthogonal if… read more

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What is jerk? Jerk is to acceleration as acceleration is to velocity. And, acceleration is to velocity as velocity is to position. So let’s start there. The instantaneous velocity at which you travel tells you… read more

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This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. For the specific case of a filter, the frequency response tells you exactly how each frequency is altered. The example code is… read more